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Journal of Mathematical Sciences

, Volume 196, Issue 4, pp 498–514 | Cite as

Linear Methods in the Proof of Jackson Type Inequalities and Applications to Estimates of Functionals with Two Known Moments

  • O. L. VinogradovEmail author
  • V. V. Zhuk
Article

We propose a new method for estimating functionals in terms of higher order moduli of continuity with explicit constants. Using this method, we estimate deviations of linear methods of approximation by entire functions of finite degree and, in particular, by trigonometric polynomials. For illustration of the results, we derive estimates for the Riesz and Akhiezer–Krein–Favard averages. Bibliography: 14 titles.

Keywords

Entire Function Trigonometric Polynomial Conjugate Function Primitive Function Riesz Operator 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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